Guillermo is a professional deep water free diver. His altitude (in meters relative to sea level), $x$ seconds after diving, is modeled by $g(x)=\dfrac{1}{20}x(x-100)$ How many seconds after diving will Guillermo reach his lowest altitude?
Solution: Guillermo's altitude is modeled by a quadratic function, whose graph is a parabola. The lowest altitude is reached at the vertex. So in order to find when that happens, we need to find the vertex's $x$ -coordinate. The vertex's $x$ -coordinate is the average of the two zeros, so let's find those first. $\begin{aligned} g(x)&=0 \\\\ \dfrac{1}{20}x(x-100)&=0 \\\\ \swarrow &\searrow \\\\ \dfrac{1}{20}x=0\text{ or }&x-100=0 \\\\ x={0}\text{ or }&x={100} \end{aligned}$ Now let's take the zeros' average: $\dfrac{({0})+({100})}{2}=\dfrac{100}{2}=50$ In conclusion, Guillermo will reach his lowest altitude $50$ seconds after diving.